Inferring Trade-Offs in University Admissions: Evidence from Cambridge

How do elite universities balance diversity and academics during admissions? We develop a theory-based empirical framework to identify and quantify this potential trade-off, using postentry outcomes. We apply this to matched admission and exam-performance data from Cambridge. Comparing first- versus second-round admits from different demographic groups yields bounds on the trade-off magnitude, which (a) hold irrespective of whether we observe all applicant characteristics and (b) require no information on rejected applicants. We find robust evidence of trade-off between gender balance and future performance in math-intensive subjects but not for state/private school students or for gender in competitive nonmathematical disciplines.